Offering 100 points to the first correct answer. Need asap, please!

A rectangle has sides measuring (6x + 4) units and (2x + 11) units.

Part A: What is the expression that represents the area of the rectangle? Show your work. (4 points)

Part B: What are the degree and classification of the expression obtained in Part A? (3 points)

Part C: How does Part A demonstrate the closure property for polynomials? (3 points)

An expression that represents the amount of canned food collected so far by the three friends is 8x² + 2xy - 4.

An expression that represents the number of cans the friends still need to collect to meet their goal is 4x² - 4xy + 2.

From the information provided above, we can logically deduce the following number of canned food collection expressions for each friend:

Jessa; 3x²

Tyree: 5x² - 8

Ben: 2xy + 4

Canned food collection goal: 12x² - 2xy - 2

Therefore, an expression that represents the total amount of canned food collected so far by the three friends can be calculated and written as follows;

Total amount collected so far = 3x² + 5x² - 8 + 2xy + 4

Total amount collected so far = 8x² + 2xy - 4

In order to meet the goal, they need to collect this amount:

Remaining canned foods = 12x² - 2xy - 2 - (8x² + 2xy - 4)

Remaining canned foods = 12x² - 2xy - 2 - 8x² - 2xy + 4

Remaining canned foods = 4x² - 4xy + 2

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The pairs of angles that are supplementary angles include the following:

SQT and SQR = Option B

TQP and RQP = Option C

SQR and RQP = Option D

SQT and TQP = Option F

A supplementary angle is the angle that makes up to 180° when both are summed up together.

The angles that are chosen above include the following:

<SQT = 165°

<SQR = 15°

The addition of the both angles = 180°, and therefore is an example of a supplementary angle.

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The missing value for the quadratic function is given as follows:

y = -3.

As a function of it's roots x* and x**, the quadratic function is defined as follows:

y = a(x - x*)(x - x**)

In which a is the leading coefficient.

The roots of the function are the values of x when y = 0, hence:

x* = -4, x** = -2.

Thus:

y = a(x + 4)(x + 2)

y = a(x² + 6x + 8).

When x = 0, y = -8, hence the leading coefficient a of the function is given as follows:

8a = -8

a = -1.

Hence:

y = -x² - 6x - 8;

The missing value is the value of y when x = -1, hence:

y = -(-1)² - 6(-1) - 8

y = -3.

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We can prove that the quadratic equation x² + (1 - k)x + k - 3 = 0 has two real roots for all real values of k.

The discriminant of the quadratic equation ax² + bx + c = 0 is given by Δ = b² - 4ac.

If Δ is positive, the equation has two real roots. If Δ is zero, the equation has one real root. If Δ is negative, the equation has two complex roots.

For the given equation, x² + (1 - k)x + k - 3 = 0, we can find the discriminant:

Δ = (1 - k)² - 4(k - 3)

= 1 - 2k + k² - 4k + 12

= k² - 6k + 13

To show that the roots are real for all real values of k, we need to show that Δ ≥ 0 for all k.

Δ = k² - 6k + 13

= (k - 3)² + 4

Since the square of any real number is non-negative, we have (k - 3)² ≥ 0. Therefore, Δ = (k - 3)² + 4 ≥ 4 for all real values of k.

Since Δ is always positive or zero, the quadratic equation x² + (1 - k)x + k - 3 = 0 has two real roots for all real values of k.

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The value of -5/6 ÷( -1/4) is 3 1/3

A fraction is a part of a whole. it consist of upper part( numerator) and lower part denominator.

In a simple fraction, both numerator and denominator are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

Solving -5/6 ÷( -1/4)

-5/6 × -4/1

= 20/6

= 10/3

= 3 1/3

therefore the value of the expression is 3 1/3

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Answer:

events at A and B are independent because P(A)(B)≠P(A)

Answer:

Rice:Water = 1:2

Step-by-step explanation:

One of the stages in Cooley's looking-glass self theory is A. We imagine how we look to other people.

As per Cooley's theory, our self-concept is shaped through a social interchange in which we envision how others perceive us, evaluate that perception and then deliberate on how those assessments influence our self-esteem.

All these components are part of the "looking-glass self" process, consisting of three stages: 1) fantasising about how one appears to others 2) pondering over the judgments made based on appearance and 3) evolution of the self-image influenced by such judgements. Notably, imagining one's outward persona forms an integral element of this psychological principle.

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A. The slope of the linear function is given as follows: m = 2.

B. The slope means that the number of races increases by two when the number of track meets increases by one.

C. The y-intercept of 5 means that when there are 5 races when there are 0 track races.

D. The slope-intercept definition of the linear function is given as follows: y = 2x + 5.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The input and output variables for this problem are given as follows:

Two points in the function are given as follows:

(0,5) and (1,7).

Hence the slope and the intercept are given as follows:

Meaning that the function is defined as follows

y = 2x + 5.

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Te polynomials are closed under addition and subtraction

This is calculated as

Length 1 and 2 = 8x^2 − 5x − 2 + 7x − x^2 + 3

Evaluate

Length 1 and 2 = 7x^2 + 2x + 1

This is calculated as

Third side = Perimeter - Length 1 and 2

So, we have

Third side = 4x^3 − 3x^2 + 2x − 6 - 7x^2 - 2x - 1

Evaluate

Third side = 4x^3 − 10x^2 − 7

Yes, the answers for Part A and Part B show that the polynomials are closed under addition and subtraction

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The values of the variables x and y for the cyclic quadrilateral are 9 and 17 respectively.

The figure is a cyclic quadrilateral since it four side vertices lie on the circumference of the circle. The sum of the interior angles of a cyclic quadrilateral is also 360°. Also opposite angles of a cyclic quadrilateral add up to 180°

Thus;

11x + 8 + 8x + 1 = 180° {opposite angles of a cyclic quadrilateral}

19x + 9 = 180°

19x = 180° - 9 {collect like terms}

19x = 171

x = 171/19

x = 9

Also;

6y - 4 + 5y - 3 = 180°

11y - 7 = 180°

11y = 180 + 7

11y = 187

y = 187/11

y = 17

Therefore, the values of the variables x and y for the cyclic quadrilateral are 9 and 17 respectively.

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The line equations according to its features are, respectively:

Case C: y = - 2

Case D: x = - 7

Case E: y = - x + 1 / 2

Case F: y = - (1 / 3) · x + 20 / 3

Case G: y = 4 · x + 17

In this question we must determine five line equations based on its features. The equation of the line can be found by understanding the following features:

There are two forms of the equation of the line:

Slope-intercept

y = m · x + k

Standard

a · x + b · y + c = 0

Where:

Now we proceed to determine the equation of each line:

Case C: m = 0, (x, y) = (- 7, - 2)

- 2 = 0 · (- 7) + k

k = - 2

y = - 2

Case D: m = 0, (x, y) = (- 7, - 2)

x = - 7

Case E: k = 1 / 2, m = - 1

y = - x + 1 / 2

Case F: Parallel to x - 3 · y = 9, (x, y) = (2, 6)

x - 3 · y = 9

3 · y = 9 - x

y = 3 - (1 / 3) · x

m = - 1 / 3

6 = - (1 / 3) · 2 + k

6 = - 2 / 3 + k

k = 20 / 3

y = - (1 / 3) · x + 20 / 3

Case G: Perpendicular to y + (1 / 4) · x - 5 = 0, (x, y) = (- 3, 5)

y + (1 / 4) · x - 5 = 0

y = - (1 / 4) · x + 5

m = - 1 / 4

m' = 4

5 = 4 · (- 3) + k

5 = - 12 + k

k =  17

y = 4 · x + 17

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Answer:

k = 1

Step-by-step explanation:

given a polynomial f(x) divided by (x + h) with a remainder of 0 , then (x + h) is a factor of f(x) and f(- h) = 0

here the polynomial is divided by (x + 1)

then substitute x = - 1 into the polynomial and equate to zero

k(- 1)³ + (- 1)² - 5(- 1) - 5 = 0

- k + 1 + 5 - 5 = 0

- k + 1 = 0 ( subtract 1 from both sides )

- k = - 1 ( multiply both sides by - 1 )

k = 1

Answer:

What do we have to do in this? Find x? Let me know I'll explain it in the comment section

The volume of the resulting solid revolved around the x-axis is equal to  28.274 cubic units (round to the nearest thousandth).

Vertices of the right triangle are,

(0, 0), (0, 3) and (-4, 0)

To obtain the solid formed by revolving the given right triangle about the x-axis, use the disk method.

The cross-sectional area of the solid at a given height is a circle with radius = distance between the x-axis and the upper edge of the triangle at that height.

The height of the triangle is 3 units,

and the base of the triangle is 4 units.

So, the equation of the hypotenuse of the right triangle can be found as follows,

y = (3/4)x + 3

Now, let us consider a horizontal slice of the solid at a distance y units above the x-axis.

The radius of the circle at this height is ,

r = y - 3

The area of the circle at this height is ,

A = πr²

   = π(y - 3)²

The limits of integration are y = 0 the x-axis to y = 3 the height of the triangle.

Using the disk method, the volume of the solid is,

V = [tex]\int_{0}^{3}[/tex] π(y - 3)²dy

Evaluating the integral, we get,

⇒ V = π /3 ( y - 3 )³[tex]|_{0}^{3}[/tex]

⇒ V = π/3 [( 3- 3 )³ - ( 0 -3)³ ]

⇒ V = (π /3) ( 27)

⇒V  = 9π

⇒V  = 9 (3.1415)

Rounding to the nearest thousandth gives,

V ≈ 28.274

Therefore, the volume of the solid formed by revolving the given right triangle about the x-axis is approximately 28.274 cubic units.

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The function value of f(f(7)) is -13.

We have,

x     9   -11    7   11      -6   -13

f(x)  11    4   -6   -1    -15    -5

From the table,

Using the given table, we can see that:

f(93) is not in the list of x values, so we cannot find its inverse.

Therefore,

We cannot evaluate [tex]f^{-1}(f(93)).[/tex]

f(7) is in the list of x values, and its corresponding function value is f(7) = -6. Therefore,

We can evaluate f(f(7)) by finding the function value corresponding to -6.

i.e

f(-6) = -13

Now,

The function value of f(f(7)).

= f(-6)

= -13

Thus,

The function value of f(f(7)) is -13.

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Triangle GHI is similar to triangle SQR. Therefore, option A and E are correct answers.

Given that, in triangle GHI, ∠G=104°, ∠H=45° and ∠I=31°.

In triangle QRS, ∠Q=45°, ∠R=31° and ∠S=104°.

In triangle XYZ, ∠X=104°, ∠Y=45° and ∠Z=31°.

Consider triangle GHI and triangle QRS

∠G=∠S=104°

∠H=∠Q=45°

∠I=∠R=31°

ΔGHI is similar to ΔSQR

Consider triangle XYZ and triangle QRS

∠X=∠S=104°

∠Z=∠Q=45°

∠Y=∠R=31°

ΔXYZ is similar to ΔSRQ

Consider triangle XYZ and triangle GHI

∠X=∠G=104°

∠Z=∠H=45°

∠Y=∠I=31°

ΔXYZ is similar to ΔGIH

Therefore, option A and E are correct answers.

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One way Olivia might have moved ABCDE onto A"B"C"D"E" is by first reflecting ABCDE over the x-axis, and then translating it 4 units to the left and 6 units down.

1) This would map point A to A", B to B", C to C", D to D", and E to E", creating A"B"C"D"E".

2) Angelica's transformation does not result in a figure that matches A"B"C"D"E". Reflecting ABCDE over the y-axis would map point A to A", B to E", C to D", D to C", and E to B", so the shape would be flipped horizontally. Translating it up 8 units would then shift the shape up, but it would still be horizontally flipped, so it would not match A"B"C"D"E".

3) Michael's claim is not correct. Translating ABCDE diagonally 8 units up and 10 units right would move point A to point J, which is not on A"B"C"D"E". The other points would also not be in their correct positions, so the resulting shape would not match A"B"C"D"E". To get to A"B"C"D"E" with one transformation, Michael would need to use a combination of translation, rotation, and/or reflection.

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Freezer B is better to buy in terms of dollars per cubic foot.

We have,

Dimensions of Freezer A = 1 ft x 1 ft x 5 ft

Sale price of Freezer A = $499.99

Dimensions of Freezer B = 1.5 ft x 1.5 ft x 4 ft

Sale price of Freezer B = $149.99

Now, Dollars per cubic foot for Freezer A

= (1 x 1 x 5)/ 499.99

= 0.01

and, Dollars per cubic foot for Freezer B

= (1.5 x 1.5 x 4)/ 149.99

= 0.06

Thus, Freezer B is better to buy in terms of dollars per cubic foot.

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The volume of the rectangular prism is 90 units³

We have,

The figure shown has the dimensions:

L = Length = 5 units

W = Width = 6 units

H = Height = 3 units

Now,

The volume of the rectangular prism.

= L x W x H

= 5 x 6 x 3

= 90 units³

Thus,

The volume of the rectangular prism is 90 units³

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Answer:

The company charged $500 for its services,and Mia gives the movers a 16% tip. Now, we can add the tip amount to the cost of the service to find the total amount Mia paid: Total amount = Cost of service + Tip amount = $500 + $80 = $580

Step-by-step explanation:

The value of x in the intersecting secants in a circle is 0.5

From the question, we have the following parameters that can be used in our computation:

intersecting secants

Using the theorem of intersecting secants, we have teh following equation

2 * (x + 2) = 1 * (1 + 4)

Evaluating the like terms

So, we have

2 * (x + 2) = 1 * 5

Divide both sides by 2

This gives

x + 2 = 2.5

Evaluating the like terms

So, we have

x = 0.5

Hence, the value of x is 0.5

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The solution to the system of linear equations, would be :

We can rewrite the system of linear equations to be:

x + 0 y + z = - 1

0 x + y + 4 z = - 4

0x + 0y + 0z = 0

The simple version is:

x + z = -1

y + 4z = -4

0 = 0

Therefore, the solution can be written as:

x = -1 - z

y = -4 - 4z

z = z

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The volume of the file cabinet in this problem is given as follows:

V = 8 and 7/10 cu ft.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:

Volume = length x width x height.

The dimensions for this problem are given as follows:

2.167 ft, 1.5 ft and 2.67 ft.

Hence the volume of the prism is given as follows:

V = 2.167 x 1.5 x 2.67

V = 8.7 ft³.

As a mixed number, the volume is given as follows:

V = 8 and 7/10 cu ft.

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The general solution to the differential equation based on the information is y(x) = (1/2) x^4 e^(-3x) + C e^(-3x)

Based on the information, dy/dx + 3y = 2x³ e^(-3x)

The integrating factor is e^(∫3 dx) = e^(3x),

e^(3x) dy/dx + 3e^(3x) y = 2x^3 e^(3x - 3x)

d/dx (e^(3x) y) = 2x^3

e^(3x) y = ∫2x^3 dx = (1/2)x^4 + C

C is an arbitrary constant of integration.

y = (1/2) x^4 e^(-3x) + C e^(-3x)

The equation will be y(x) = (1/2) x^4 e^(-3x) + C e^(-3x)

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The measure of angle A in triangle ABC is approximately 113.8 degrees.

To find the measure of angle A (LA) in triangle ABC, we can use the Law of Cosines:

c² = a² + b² - 2ab*cos(C)

where c is the length of the side opposite to angle C, and a and b are the lengths of the other two sides.

In this case, we want to find LA, which is opposite to side a (BC). So we can rewrite the Law of Cosines as:

cos(A) = (b² + c² - a²) / 2bc

Plugging in the values we have:

cos(A) = (24.1² + 15.7² - 25.3²) / (2 * 24.1 * 15.7)

cos(A) = -0.3694

Now we need to find the inverse cosine (cos⁻¹) of -0.3694 to get the measure of angle A:

A = cos⁻¹(-0.3694)

Using a calculator, we get:

A ≈ 113.8 degrees

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The area of the desktop is 307.72 square inches.

Remember that the area of a semicircle of radius R is given by the formula:

A = (pi/2)*R²

Where pi = 3.14

Here we know that the diameter is 28 inches, then the radius is:

R = 28in/2 = 14 inches

Replacing that in the formula for the area we will get:

A=  (3.14/2)*(14 in)²

A = 307.72 in²

That is the area of the desktop.

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